This man, along with Burmann, names a formula that gives a Taylor expansion of an inverse function of an analytic function. This man's identity allows one to prove the Cauchy-Schwarz Inequality via the squares of real numbers being positive. He also names a theorem stating that every positive integer can be written as a sum of at most four squares. Another theorem named for him states that the order of a subgroup must divide the order of a group. With Euler, he names a differential equation fundamental to the (*) calculus of variations, and his name is given to the remainder term in a Taylor Expansion. He further lends his name to quantities useful in finding extrema
This man, along with Burmann, names a formula that gives a Taylor expansion of an inverse function of an analytic function. This man's identity allows one to prove the Cauchy-Schwarz Inequality via the squares of real numbers being positive. He also names a theorem stating that every positive integer can be written as a sum of at most four squares. Another theorem named for him states that the order of a subgroup must divide the order of a group. With Euler, he names a differential equation fundamental to the (*) calculus of variations, and his name is given to the remainder term in a Taylor Expansion. He further lends his name to quantities useful in finding extrema of multivariate functions under certain constraints; those quantities are denoted by lambda. For ten points, name this French polymath known for his multipliers.
This man, along with Burmann, names a formula that gives a Taylor expansion of an inverse function of an analytic function.
Joseph-Louis {Lagrange}